"There were significant casualties on both sides, but more on the Eritrean side," Ethiopian government spokesman Getachew Reda told AFP.
He said the battle that began Sunday was one of the most serious in recent years, noting that while the two sides had exchanged gun fire in the past, this clash was on a far larger scale. The fighting had reportedly calmed on Monday.
"We used to take precautionary measures against this regime, but this time was much more important in terms of magnitude than the measures that were taken so far," Getachew added.
Ethiopia yesterday "unleashed an attack against Eritrea on the Tsorona Central Front," Eritrea's ministry of information said in a statement.
More From This Section
Getachew instead claimed the fighting started when Eritrean artillery fired shells across the border.
"Eritrean forces started shelling our positions, including civilian ambulances, and we responded," said Getachew, who had initially claimed no knowledge of the fighting.
Eritrea won independence from Ethiopia in 1991 after three decades of war, but returned to battle in 1998-2000.
The two remain bitter enemies, with their troops still eyeing each other along the fortified frontier. Tensions are never far from the surface.
Eritrea and Ethiopia have long traded accusations of attacks and of backing rebels to needle each other.
In March 2012, Ethiopia attacked an Eritrean military base, accusing the country of supporting "terrorist activities" on its territory.
In February, Ethiopia accused Eritrea of being behind anti-government protests in the Oromia region last year which led to a violent clampdown by the government in Addis Ababa.
The two countries remain at odds over the flashpoint town of Badme, awarded to Eritrea by a United Nations-backed boundary commission but still controlled by Ethiopia.
Eritrea's media is ranked below North Korea as worst in the world for press freedom by Reporters Without Borders.
However, opposition Eritrean websites, run from abroad but with contacts inside the country, reported there were clashes along the border.